exactextractr is an R package that quickly and accurately summarizes raster values over polygonal areas, commonly referred to as zonal statistics. Unlike most zonal statistics implementations, it handles grid cells that are partially covered by a polygon. Typical performance for real-world applications is orders of magnitude faster than the raster package.

Example Graphic.

Calculations are performed using the C++ exactextract tool. Additional background and a description of the method is available here. Full package reference documentation is available here.

Basic Usage

The package provides an exact_extract method that operates analogously to the extract method in the raster package. The snippet below demonstrates the use of this function to compute a mean December precipitation for each municipality in Brazil.

library(raster)
library(sf)
library(exactextractr)

# Pull municipal boundaries for Brazil
brazil <- st_as_sf(getData('GADM', country='BRA', level=2))

# Pull gridded precipitation data
prec <- getData('worldclim', var='prec', res=10)

# Calculate vector of mean December precipitation amount for each municipality
brazil$mean_dec_prec <- exact_extract(prec[[12]], brazil, 'mean')

# Calculate data frame of min and max precipitation for all months
brazil <- cbind(brazil, exact_extract(prec, brazil, c('min', 'max')))

Summary Operations

exactextractr can summarize raster values using several pre-defined operations as well as arbitrary R functions. Pre-defined operations are specified by providing one or more operation names to the fun parameter of exact_extract.

The following summary operations are supported:

Name Description
count Sum of all cell coverage fractions.
majority (or mode) The raster value with the largest sum of coverage fractions.
max Maximum defined value of cells that intersect the polygon, ignoring coverage fractions.
mean Mean defined value of cells that intersect the polygon, weighted by the percent of the cell that is covered.
min Minimum defined value of cells that intersect the polygon, ignoring coverage fractions.
minority The raster value with the smallest sum of coverage fractions.
sum Sum of defined values of raster cells that intersect the polygon, with each raster value weighted by its coverage fraction.
variety The number of distinct raster values in cells wholly or partially covered by the polygon.

Two additional summary operations require the use of a second weighting raster, provided in the weights argument to exact_extract

Name Description
weighted_mean Mean defined value of cells that intersect the polygon, weighted by the product of the coverage fraction and the value of a second weighting raster.
weighted_sum Sum of defined values of raster cells that intersect the polygon, multiplied by the coverage fraction and the value of a second weighting raster.

These operations are described in more detail below.

Weighting / Geographic Coordinates

exact_extract allows for calculation of summary statistics based on multiple raster layers, such as a population-weighted temperature. For the weighted_mean and weighted_sum operations, this is as simple as providing a weighting RasterLayer to the weights argument of exact_extract. The weighting raster must use the same coordinate system as the primary raster, and it must use a grid that is compatible with the primary raster. (The resolutions and extents of the rasters need not be the same, but the higher resolution must must be an integer multiple of the lower resolution, and the cell boundaries of both rasters must coincide with cell boundaries in the higher-resolution grid.)

One application of this feature is the calculation of zonal statistics on raster data in geographic coordinates. The previous calculation of mean precipitation amount across Brazilian municipalities assumed that each raster cell covered the same area, which is not correct for rasters in geographic coordinates (latitude/longitude).

We can correct for varying cell areas by creating a second raster with the area of each cell in the primary raster, and using this raster in a weighted_mean summary operation. (The area function from the raster package will calculate the cell areas for us.)

brazil$mean_dec_prec_weighted <- exact_extract(prec[[12]], brazil, 'weighted_mean', weights=area(prec))

With the relatively small polygons used in this example, the error introduced by assuming constant cell area is negligible. However, for large polygons that span a wide range of latitudes, this may not be the case.

Summary Functions

In addition to the summary operations described above, exact_extract can accept an R function to summarize the cells covered by the polygon. Because exact_extract takes into account the fraction of the cell that is covered by the polygon, the summary function must take two arguments: the value of the raster in each cell touched by the polygon, and the fraction of that cell area that is covered by the polygon. (This differs from raster::extract, where the summary function takes the vector of raster values as a single argument and effectively assumes that the coverage fraction is 1.0.)

An example of a built-in function with the appropriate signature is weighted.mean. Some examples of custom summary functions are:

# Number of cells covered by the polygon (raster values are ignored)
exact_extract(rast, poly, function(values, coverage_fraction)
                            sum(coverage_fraction))

# Sum of defined raster values within the polygon, accounting for coverage fraction
exact_extract(rast, poly, function(values, coverage_fraction)
                            sum(values * coverage_fraction, na.rm=TRUE))

# Number of distinct raster values within the polygon (coverage fractions are ignored)
exact_extract(rast, poly, function(values, coverage_fraction)
                            length(unique(values)))

# Number of distinct raster values in cells more than 10% covered by the polygon
exact_extract(rast, poly, function(values, coverage_fraction)
                            length(unique(values[coverage_fraction > 0.1])))

A multi-raster summary function can also be written to implement complex weighting behavior not captured with the weighted_mean or weighted_sum summary operations. If exact_extract is called with a RasterStack instead of a RasterLayer, the R summary function will be called with a data frame of raster values and a vector of coverage fractions as arguments. Each column in the data frame represents values from one layer in the stack, and the columns are named using the names of the layers in the stack.

A more verbose equivalent to the weighted_mean usage demonstrated could be written as:

stk <- stack(list(prec=prec[[12]], area=area(prec)))

brazil$mean_dec_prec_weighted <-
  exact_extract(stk, brazil, function(values, coverage_frac)
                               weighted.mean(values$prec, values$area*coverage_frac, na.rm=TRUE))

Note that the assembly of a RasterStack to use an R summary function requires that the primary and weighting rasters share an extent and resolution, a limitation not shared by the named summary operations.

Rasterization

exactextractr can also rasterize polygons though computation of the coverage fraction in each cell. The coverage_fraction function returns a RasterLayer with values from 0 to 1 indicating the fraction of each cell that is covered by the polygon. Because this function generates a RasterLayer for each feature in the input dataset, it can quickly consume a large amount of memory. Depending on the analysis being performed, it may be advisable to manually loop over the features in the input dataset and combine the generated rasters during each iteration.

Performance and Accuracy

An example benchmark using the example data is shown below. The mean execution time for exactextractr was 2.6 seconds, vs 136 for raster. Timing was obtained from execution on an AWS t2.medium instance.

microbenchmark(
  a <- exact_extract(prec[[12]], brazil, weighted.mean),
  b <- extract(prec[[12]], brazil, mean, na.rm=TRUE), times=5)

# Unit: seconds
#               expr         min          lq        mean     median          uq        max neval
# a <- exact_extract(...)    2.5674   2.586868   2.626761   2.587283   2.613296   2.778957     5
#       b <- extract(...)  136.1710 136.180563 136.741275 136.226435 136.773627 138.354764     5

Although exactextractr is fast, it is still several times slower than the command-line exactextract tool.

Results from exactextractr are more accurate than other methods because raster pixels that are partially covered by polygons are considered. The significance of partial coverage increases for polygons that are small or irregularly shaped. For the 5500 Brazilian municipalities used in the example, the error introduced by incorrectly handling partial coverage is less than 1% for 88% of municipalities and reaches a maximum of 9%.

Dependencies

Installation requires version 3.5 or greater of the GEOS geometry processing library. It is recommended to use the most recent released version (3.8) for best performance. On Windows, GEOS will be downloaded automatically as part of package install. On MacOS, it can be installed using Homebrew (brew install geos). On Linux, it can be installed from system package repositories (apt-get install libgeos-dev on Debian/Ubuntu, or yum install libgeos-devel on CentOS/RedHat.)